324 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



Thus, it seems that the former, 10 , modulus is typical of the struc- 

 tural arrangements in polymers said to be above their second order 

 transition temperatures^ ' ^ while the second, 10^, modulus reflects in- 

 teractions below the freezing-in. 



These conclusions obtain regardless of the particular expression of the 

 data. But, for comparison, curves are shown on Fig. 5 for a polyiso- 

 butylene A" in which the dynamic modulus n at 20 kc is computed for 

 both Maxwell and Voigt elements. The two points denoting the steady 

 flow viscosity of polymer A" rank it with respect to the others in the 

 series. 



Apparently even very fluid polymer melts, chaui molecule plasticizers, 

 and small segments of long molecules must be expected to show appre- 

 ciable rigidity when stressed rapidly. Referring to the introduction it is 

 reasonable that rough extrusions, frozen-in molding stresses and the 

 like are so easily produced. The lines of Fig. 5 are not, of course, implied 

 to be linear over any considerable temperature range. In the region rep- 

 resented, the temperature coefficient for viscous flow is about 16 kcal 

 for the B, C and D liquids (about 12 for A). This agrees roughly with 

 the steady flow values found for very high molecular Aveight polyiso- 

 butylene. ' "'^ The temperature coefficient for the rigidity is less, as 

 would be expected, since the whole center of gravity of the chain need 

 not be displaced, but only local segments. 



This quasi-configurational elasticity is increased by molecular weight 

 (although kinetic theory elasticity of chain segments in a network is de- 

 creased by increasing segment length). The log m vs density at 25°C 

 plotted in Fig. 6 indicates that the chief influence is the number of 

 chains per cc, since the points for all the molecular weights now lie on 

 a single line. It should be repeated that the elasticity modulus plotted, 

 H, is again for a roughly frequency-independent or "absolute" model."' " 

 The same is true for the three solid lines on Fig. 6, showing ju in the 

 second, or 10 cycle, relaxation range. Here effects of detailed liquid 

 structure come out; the three average molecular weights no longer lie 

 so nearly on a single line. This elasticity is presumably from the crystal- 

 like interaction of nearest-neighbor segments. If temperature is adjusted 

 so that densities are the same, it is seen that the lower average molecular 

 weight liquid has the higher elasticity modulus. This difference is not 

 large, and should not be interpreted as showing an equal segment inter- 

 action, for a polymer of lower specific volume (B compared to D). 

 Rather, it emphasizes in this relaxation range, approaching the "glass" 

 behaviour, that the relaxation rate is vastly more temperatiu'o dei^endent 

 than the specific volume change alone, and structural variations in the 



